FERMI PROBLEMS WKSHT

HONORS PHYSICS

NAME.:

9-Sep-Ll

Enrico Fermi was one of the scientists who worked on developing the first atomic bomb andwas known in the field for his ability to use approximations and assumptions to slice through aquagmire of calculations to get a quick and simple answer. One typical example of this wasdemonstrated during the detonation of that first bomb at Alamogordo, New Mexico, in July1945. As the first tremors of the shock wave reached the observers, Enrico dropped a handful oftorn bits of paper from over his heah. The wind rushing past as the shock *urr" pur*"d by blewthe bits of paper about 2.5 yards behind him. He thought for a moment and thenboldlyannounced that the blast released the energy equivalent to 10,000 tons of TNT. Analysis of thereadings from sensitive instruments located around the site took several weeks to analyze. Theresults confirmed Fermi's proclamation"

Though Fermi's grasp of math and physics is well beyond ours, the basic techniques he usedare not. Enrico used an approximation technique similar to the one you have just used, plus awealth of background knowledge. As you gain experience in working with physicr, yorr.background knowledge will grow, enabling you to solve seemingly difficult calculations on the'back of an envelope'. For instance:

The distance from New York City to San Francisco is about 3000 miles. The sun rises in SanFrancisco three hours later than it does in New York. GryC is on ,Eastern, time, we are on'Central' time, Salt Lake City is on 'Mountain' time and San Francisco is on 'pacific' time).Knowing this, what is the circumference of the earth?

The distance is 3000 mi and the time difference is 3 hrs. The time it takes for the earth to spincompletely around is 24 hrs. Set up a proportion and solve it.

3000 mi3 hrs

: Xmi24hrs

Try these on your own -1. If the moon has a diameter of 3.48 x 106 m and is exactly covered up by your thumb held at

arm's length, how far away is the moon? (Hint: you need a meter-stick or a tape-measure forthis one)

If the sun is 1.49 x 10i1 m away, and is exactly covered up by your thumb held at arm,slength, what is its diameter? (Hint: you need a meter-stick or tape measure for this one, too.)

If the sun is 1.49 x 1011 m away from the earth, how many meters does the earth travel in itsorbit each day? (Hint: what is the circumference of a circle?)

2.

J.

In making stab-in-the-dark guesses, generally, the errors made in one approximation often cancel

the errors made in another approximation. True Fermi problems have no definite answer, onlyball-park answers, and anyone can make the basic assumptions.

For instance, Fermi once posed this problem to his students at the Univ. of Chicago:

How many piano tuners are in Chicago (a city of 3,000,000 people)?

Go on! Take a stab at it! You might start by guessing at how many people are in ahousehold pnd what fraction of those households have pianos and how often they tunetheir pianos and how many pianos a tuner can tune in a day and how many he could tunetn ayear and how many tuners it wouid take to tune the pianos needing tuning this year.

Once you have an answer, go on-line and use Yellow Pages to search for "piano tuner" inChicago.

Frank Drake did a similar problem (in 1960) by approximating how many other planets in ourgalaxy might harbor intelligent life, and that we could communicate with. We'I1 save that one

for a class exercise.

Here are some others that you might try:

' 1. How many square meters 1m2) of pizzawtll the EHS Cafeteria bake this school year?

2" How many jelly beans will fit in a one-liter jar?

3. How many inflated party balloons will it take to fil1the Chemistry ciassroom?

4. How much heavier is the high school when all the students and staff are here?

5. How many golf-balls will fit inside a suitcase?

6. How many gallons of gasoline are used just by cars in the USA each year?

7. If you stacked one-dollar bil1s on top of each other, how high would the stack have to be tohold the USA's National Debt of $14,684,035,400,000 (at 11:00 pm 3 SEP 11)?

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i. The mass of how many Ford Falcons is equal to the mass of the water in the swirnmingpool at the Brisbane Girls' Grammar School in Australia?

(Based on iesson plan by Summer '96 Math Forum Institute Peter Moulds)

2. How many jelly beans fil1 a one-liter jar?

3. What is the mass in kilograms of the student body in your school?

4. How many golf balls will fillin a suitcase?

You might want to first assume that the diameter of the golf ball is 1". An extension tothe probldn would be: How many ba1ls with a2" diameter would it take to frll thesuitcase?

5. How many gallons of gasoline are used by cars each year in the United States?

6. How high would the stack reach if you piled on trillion dollar bi11s in a single stack?

7. Approximately what fraction of the area of the continental United States is covered byautomobiles?

8. How many'hairs are on your head?

9. What is the weight of solid garbage thrown away by American families every year?

10. if your life earnings were doled out to you at a certain rate per hour for every hour ofyour life, how much is your time worth?

1 1. How many cells are there in the human body?

12. How many individual frames of film are needed for a feature-length fiim? How long is

such a fi1m?

The following questions were developed by K-12 students

13. How many water balloons will it take to fill the school gymnasium?

14. How many flat toothpicks would fit on the surface of a sheet of poster board?

15. How many hot dogs will be eaten at major league baseball games during a one year

season?

16. How many revolutions will a wheel on the bus make during our seventh grade trip fromBaton Rouge, LA to Washington, D.C.?

17. How many minutes willbe spent on the phone by middle school students in the UnitedStates?

18. How many pLzzaswill be ordered in your state this year?